1. Field of the Invention
This invention relates to acoustooptic apparatus, and more particularly to such apparatus for modulating and diffracting a plurality of beams of different optical wavelenghts such that (1) the diffracted beams scan the same angular range at different scan rates with modulating signals for each beam synchronized to that beam's scan rate and (2) selecting diffracting frequency ranges commensurate with a predetermined maximum variation in diffraction efficiency.
2. Description of the Prior Art
When light beams of different wavelengths are deflected by an acoustooptic device to which an acoustic wave of varying frequency f is applied, the longer wavelength beam will scan a larger deflection angle than the shorter wavelength light for the same acoustic frequency bandwidth .DELTA.f. As background for the following description, it is well known that when an acoustic wave of frequency f and velocity v interacts with a light beam of wavelength .lambda., the acoustic wave acts as a diffraction grating which deflects the beam. The angle between the incident beam and the acoustic wavefront is .theta..sub.i. For deflection in optically isotropic material, and where the distance across the acoustic wave is greater than (v/f).sup.2 /.lambda., the incident light is diffracted only in the first order. This phenomenon is called Bragg reflection, and the incident angle .theta..sub.i which satisfies the following equation is called the Bragg angle .theta.: EQU sin .theta. = .lambda.f/2v (1)
The Bragg angle .theta. is that angle which gives the maximum diffraction efficiency at a given acoustic wave input frequency.
In FIG. 1 (in which are shown an acoustooptic medium A, a transducer T, an input laser beam B.sub.1, an undiffracted beam B.sub.2, and a diffracted beam B.sub.3), the angles of incidence .theta..sub.i and output .theta..sub.o are defined. If .theta..sub.i is maintained at less than 1.degree., sin .theta..sub.i can be approximated by .theta..sub.i and the angle of incidence of the light beam is given by: EQU .theta..sub.i = .lambda.f.sub.c /2v + .delta. (2)
where f.sub.c is the design frequency (nominally the center frequency of .DELTA.f) and .delta. is an offset from the Bragg angle (i.e., small positive values which broaden the operating bandwidth .DELTA.f of an acoustically beam-steered device at the expense of a midband dip in response).
In FIG. 1, the angle between the diffracted light beam B.sub.3 and the undiffracted light beam B.sub.2 is equal to .xi.f/v; therefore: ##EQU1## Since .theta..sub.o depends on the acoustic frequency f, it is possible to vary the direction of the diffracted light by changing f. If the acoustic frequency is swept through a bandwidth .DELTA.f, the diffracted beam will scan through an angular range given by: EQU .DELTA. .theta..sub.o = (.lambda./v) .DELTA.f (4)
Light beams of different selected optical wavelengths (such as for example, red, green and blue light beams) may be simultaneously applied to an acoustooptic device, each at an appropriate incident angle .theta..sub.ir, .theta..sub.ig and .theta..sub.ib, respectively, so that the diffracted beams will be collinear. However, it can be seen from equation (3) that, if the applied frequency f is swept linearly in time, the red beam will scan faster than the green beam, which in turn will scan faster than the blue beam. Hence, the diffracted beams will not remain collinear. This problem of superposition of the three beams to give a single scanning spot, i.e., achromatization, has, in the past, been solved by separating the three beams and inserting a different optical system of mirrors, prisms and/or lenses in each beam. Such a method of achromatization is described by Watson and Korpel in "Equalization of Acoustooptic Deflector Cells in a Laser Color TV System," Applied Optics, Vol. 9, pages 1176-1179 (May 1970).
A second problem occurs with respect to the selection of ranges of acoustic frequencies for different optical wavelenghts while maintaining a suitable efficiency of operation. To obtain maximum efficiency of Bragg diffraction, the incident and diffracted beams should be symmetrical with respect to the acoustic wavefronts, i.e., .theta..sub.i should equal .theta..sub.o in FIG. 1. This condition can hold strictly only for a specific applied frequency f. If, in deflecting the light, the diffracted beam angle .theta..sub.o is changed by an amount .alpha..sub.d, the angle .theta..sub.i of the incident beam should be changed accordingly to restore symmetry and maximum efficiency. However, this would require mechanical motion and defeat the purpose of an acoustooptic deflector. If no correction is made, the angle of entry is in error by 1/2 .alpha..sub.d and the lack of symmetry reduces the efficiency of the device, as explained hereinafter. More generally, the error angle .psi. is the angular difference between the direction of acoustic wave propagation (the normal to the acoustic wavefronts) and the bisector of the directions of incident and diffracted light propagation. For example, if a beam-steering acoustic transducer array is used, the direction of acoustic wave propagation changes with frequency, and the error angle .psi. will not be simply half the change in diffracted beam angle.
For specific case of a plane acoustic wave of an amplitude which is uniform throughout a width l (the optical path length across the sound beam), the useful light output would go to zero if the angle of entry were in error by v/fl; the diffracted light originating at any point within one half of the acoustic beam would then be cancelled by the light diffracted at a corresponding point in the other half, spaced l/2 from the first point. With the first nulls appearing at error angles of +v/fl, one may use +1/2(v/fl) as the limits of range of angular tolerance (see "A Television Display Using Acoustic Deflection and Modulation of Coherent Light," PROCEEDINGS OF THE IEEE, Vol. 54, No. 10, October 1966, pp. 1429-1437). This is a special case of the more general situation that when the direction of the incident light is varied, the intensity of the diffracted light will vary directly as the far field radiation pattern of the sound wave (the sound wave pattern in the acoustooptic deflector spaced from the transducer). In the case of uniform amplitude across width l, the far field acoustic power pattern P(.psi.)/P(O) as a function of the error angle .psi. (as defined above and in more detail in U.S. Pat. No. 3,860,197 is: EQU P(.psi.)/P(O) = [sin(.pi.l.psi.f/v)/(.pi.l.psi.f/v)].sup.2 ( 5)
and at the above tolerance limit of + 1/2(v/fl) the diffraction efficiency is reduced by a factor of 4/.pi..sup.2, or about 4dB. The angular range giving only a 3dB variation, which is more commonly used, is + 0.443(v/fl). For details and a more general equation for diffraction efficiency as a function of wavelength, the reader is directed to U.S. Pat. No. 3,869,197.
It can be seen from equation (2) that the design frequency f.sub.c for a given optical wavelength depends on that wavelength; i.e., the frequency f.sub.c for red light is lower than that for blue. It can also be shown, using equation (5), that the 3-dB operating ranges of acoustic frequency (as limied by the angular tolerance of the Bragg diffraction process) also depend on optical wavelength and do not coincide; they are in fact progressively offset. That is, the operating frequency range for blue light is shifted to higher frequencies than that for red, so that the useful ranges may overlap but do not fully coincide.
Since there is no way to operate a given deflector so that the 3-dB diffraction efficiency bandwidths for different optical wavelengths are simultaneously maximized and fully overlapping, only the central range of frequencies over which all wavelenghts are deflected (the range of overlap of their separate frequency responses) can normally be used. The minimum frequency is determined by the response for the shortest optical wavelength and the maximum frequency by the longest optical wavelength. This central range is normally only about 70% of the full 3-dB diffraction efficiency bandwidth for the shortest optical wavelength, resulting in (1) a significant reduction in the useful time-bandwidth product from the intrinsic capability of the device and (2) a corresponding reduction in the number of resolvable spots N of the scanned beam given by the equation EQU N = .tau..DELTA.f (6)
where .tau. is the access time, i.e., the time required for the light beam to cross the acoustic wave. The reader is referred to the PROCEEDINGS OF THE IEEE, Vol. 54, No. 10, 1966, page 1430 for a derivation of equation (6).
As an example, consider the lead molybdate deflector system disclosed in co-assigned U.S. Pat. No. 3,869,197, which issued on Mar. 4, 1975 to myself and R. N. Blazey. That device has a six transducer stepped array of l=1.8 cm and f.sub.c =187 MHz. Assuming red, green and blue incident light beams, the following table of offset angles .delta. and maximum 3-dB bandwidths were obtained by use of the equations in U.S. Pat. No. 3,869,197:
______________________________________ Min. Max. Freq. Freq. Bandwidth Color/.lambda.(.mu.m) .delta.(mrad.) (MHz) (MHz) (MHz) ______________________________________ Red/0.647 1.1 117 256 139 Green/0.521 1.0 133 291 158 Blue/0.476 0.75 141 307 166 ______________________________________
As can be seen from the table, the maximum common bandwidth for the three colors is from 141 MHz to 256 MHz (or a bandwidth of only 115 MHz) while the 3-dB diffraction efficiency bandwidths for red, green and blue are 130 MHz, 158 MHz and 166 MHz, respectively.